I was playing samurai warriors, and while viewing a map screen or something, I noticed some tiny black lines that were flickering on and off as I adjusted the 3d depth slider up and down. I couldn't quite figure out what it was, so I tried turning the 3d off altogether, and I saw what was happening.
With it in 2d mode, some of the lines were visible and some were invisible. You see, these lines were approximately 1 pixel in width. Thus, there were only shown to one eye at a time, which caused it to look weird. Turning the 3d off, it basically just shows you what you would see just with the left eye.

So basically, 3d effectively doubles the horizontal resolution of the top screen. Not a big deal, because we know that already. But conversely, 2d mode halves the horizontal resolution, meaning that some pixels wont be displayed!

If we take a grid of pixels, with 1 column of white pixels, 1 column of black, 1 column of white, and so on, all the way across, if this were to be viewed in 2d, we would see it all as a single color, not as 2 alternating colors.

If we take a grid of pixels, with 1 column of white pixels, 1 column of black, 1 column of white, and so on, all the way across, if this were to be viewed in 2d, we would see it all as a single color, not as 2 alternating colors.

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You mean as grey instead of black+white? If so, then no, it doesn't work that way. In 2D mode, a rendered image would double up every column, so you couldn't get both colors at the same time if they were alternating in that fashion.